If once can wait out for 4 or 6 hours to have their coins mixed, then waiting two block confirmations should be a problem.
I say 2 confirmations not 2 hours, just wondering because 1 confirmations needed (to avoid RBF) or 6 confirmations (to ensure it's impossible to double spend) so why two.
Maybe I wasn't elaborate enough, but my point is it is just a number, there is no major reason for 2 and not 4 or 6 confirmations. Anything more than 1 confirmation is assumed "safe" depending on the person behind the service. I have seen exchanges accept 1 confirmation in order to credit an account, Others require at least 2, 3 or 6 confirmations.
Is there anyone who has ever lost Bitcoins to a double spend attack after 1 confirmation? Personally, I have never come across such a case.
2 confirmations will definitely affect the time you have to wait for the coins to mixed, depending on how fast the blocks confirm. This is where I said that if someone can wait for 4 hours for the coins to be mixed, the 2 block confirmations (approximately 20 mins on average) should not be a big concern.